MathematicsChapter 8: Fundamentals of Trigonometry
Cosine of A Sum
cos even: cos(-B)=cos B.
Learning objectives
- State the rule or meaning of cosine of a sum in easy words.
- Apply cosine of a sum in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
Where / symbols
- COSINE OF A SUM
- cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
- COS(A+B)
- cos even: cos(-B)=cos B.
Relationship
- cos(A+B)=cos A cos B - sin A sin B
- sin(A+B)=sin A cos B + cos A sin B
Overview
Understand the idea, then apply it:
Main Idea
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
Examples cos(A+B) · Check A=B: cos 2A = cos^2-sin^2 · Keep the minus
Exam Use
Write the rule first: cos even: cos(-B)=cos B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — COSINE OF A SUM
cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
WHY — Why it matters
This rule is a separate learning unit inside compound angles: cos and sin of sums. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: cos even: cos(-B)=cos B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a cosine of a sum question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
sin(A+B) is plus both. cos(A+B) is minus on the sin product.
Key points
- even/odd
- cos(A+B)=cos A cos B - sin A sin B
- sin(A+B)=sin A cos B + cos A sin B
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Cosine of A Sum
Sticky Notes · Quick Revision
Core Idea
- cos even: cos(-B)=cos B.
What to Know
- cos even: cos(-B)=cos B. sin odd: sin(-B)=-sin B. So the + in the difference law becomes a - between the sin product.
Example or Evidence
- cos(A+B)
- Check A=B: cos 2A = cos2-sin2
- Keep the minus
How to Answer
- Write the rule first: cos even: cos(-B)=cos B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- sin(A+B) is plus both. cos(A+B) is minus on the sin product.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- cos even: cos(-B)=cos B.
- cos(A+B)
- Check A=B: cos 2A = cos2-sin2
- State the rule, show the working, and check the answer.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.